Which of the following numbers is a factor of 120? ${7,10,11,13,14}$
Answer: By definition, a factor of a number will divide evenly into that number. We can start by dividing $120$ by each of our answer choices. $120 \div 7 = 17\text{ R }1$ $120 \div 10 = 12$ $120 \div 11 = 10\text{ R }10$ $120 \div 13 = 9\text{ R }3$ $120 \div 14 = 8\text{ R }8$ The only answer choice that divides into $120$ with no remainder is $10$ $ 12$ $10$ $120$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $10$ are contained within the prime factors of $120$ $120 = 2\times2\times2\times3\times5 10 = 2\times5$ Therefore the only factor of $120$ out of our choices is $10$. We can say that $120$ is divisible by $10$.